What are the domains of applicability for the classical wave equation, the Schrödinger equation, and the Dirac equation?

Conditions

• The equations are compared based on their physical domains.
• All three are presented as equations describing the state of a wave.

Reasoning, step by step

1. Identify the classical wave equation and map it to 'macroscopic + low-speed'.
2. Identify the Schrödinger equation and map it to 'microscopic'.
3. Identify the Dirac equation and map it to 'high-speed'.
4. Note that despite different domains, all three share the common theme of describing wave states.

Example

The video lists the classical wave equation, the Schrödinger equation, and the Dirac equation as equations describing the state of a wave, distinguishing them by domain of applicability: the classical wave equation corresponds to the Newtonian viewpoint and macroscopic low-speed regimes; the Schrödinger equation corresponds to the quantum viewpoint and microscopic regimes; the Dirac equation corresponds to the relativistic viewpoint and high-speed regimes.

Common misconceptions

• Treating the three types of wave equations as equivalent equations within the same domain of applicability.
• Assuming the Schrödinger equation is only for light waves, rather than matter waves in quantum mechanics.

Watch the explanation

Explore next

• Why is it called the classical wave equation?
• How is the Schrödinger equation written in the video?